Abstract

A model is proposed for calculating mixing and chemical reactions in the limit of infinitely fast chemical kinetics and negligible heat release, in fully developed turbulent shear layers. The model is based on the assumption that the topology of the interface between the two entrained reactants in the layer, as well as the strain field associated with it, can be described by the similarity laws of the Kolmogorov cascade. The calculation yields the integrated volume fraction across the layer occupied by the chemical product, as a function of the stoichiometric mixture ratio of the reactants carried by the free streams, the velocity ratio of the shear layer, the local Reynolds number, and the Schmidt number of the flow. The results are in good agreement with measurements of the volume fraction occupied by the molecularly mixed fluid in a turbulent shear layer and the amount of chemical product, in both gas phase and liquid phase chemically reacting shear layers.

Item Type:

Report or Paper (Technical Report)

Additional Information:

Invited lecture at the United States-France Joint Workshop on Turbulent Reacting Flows, 6-10 July 1987, Rouen, FRANCE
I would like to acknowledge the many discussions within the GALCIT community, which directly or indirectly have contributed to this paper. Without wishing to imply endorsement, I would specifically like to acknowledge discussions with Dr. J. Broadwell, Prof. R. Narasimha and Prof. P. Saffman. Additionally, the critical comments by Prof. A. Leonard and Mr. P. Miller contributed to important improvements and clarifications in the final form of the text. Finally, I would like to thank Mr. C. Frieler for performing the numerical integration of the differential equation for the velocity correlation function h(c) in section 2.6. This work is part of a larger effort to investigate mixing and combustion in turbulent shear flows, sponsored by the Air Force Office of Scientific Research Contract No. F49620-79-C-0159 and Grant No. AFOSR-83-0213, whose support is gratefully acknowledged.